NAME

lgamma, lgammaf, lgammal, lgamma_r, lgammaf_r, lgammal_r, signgam - log gamma function

LIBRARY

Math library (libm, -lm)

SYNOPSIS

#include <math.h>

double lgamma(double x);
float lgammaf(float x);
long double lgammal(long double x);

double lgamma_r(double x, int *signp);
float lgammaf_r(float x, int *signp);
long double lgammal_r(long double x, int *signp);

extern int signgam;

Feature Test Macro Requirements for glibc (see feature_test_macros(7)):

lgamma():
    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L || _XOPEN_SOURCE
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

lgammaf(), lgammal():

    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

lgamma_r(), lgammaf_r(), lgammal_r():

    /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

signgam:

    _XOPEN_SOURCE
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE

DESCRIPTION

For the definition of the Gamma function, see tgamma(3).

The lgamma(), lgammaf(), and lgammal() functions return the natural logarithm of the absolute value of the Gamma function. The sign of the Gamma function is returned in the external integer signgam declared in <math.h>. It is 1 when the Gamma function is positive or zero, -1 when it is negative.

Since using a constant location signgam is not thread-safe, the functions lgamma_r(), lgammaf_r(), and lgammal_r() have been introduced; they return the sign via the argument signp.

RETURN VALUE

On success, these functions return the natural logarithm of Gamma(x).

If x is a NaN, a NaN is returned.

If x is 1 or 2, +0 is returned.

If x is positive infinity or negative infinity, positive infinity is returned.

If x is a nonpositive integer, a pole error occurs, and the functions return +HUGE_VAL, +HUGE_VALF, or +HUGE_VALL, respectively.

If the result overflows, a range error occurs, and the functions return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the correct mathematical sign.

ERRORS

See math_error(7) for information on how to determine whether an error has occurred when calling these functions.

The following errors can occur:

Pole error: x is a nonpositive integer: errno is set to ERANGE (but see BUGS). A divide-by-zero floating-point exception (FE_DIVBYZERO) is raised.
Range error: result overflow: errno is set to ERANGE. An overflow floating-point exception (FE_OVERFLOW) is raised.

STANDARDS

lgamma()
lgammaf()
lgammal(): C11, POSIX.1-2008.
signgam: POSIX.1-2008.
lgamma_r()
lgammaf_r()
lgammal_r(): None.

HISTORY

lgamma()
lgammaf()
lgammal(): C99, POSIX.1-2001.
signgam: POSIX.1-2001.
lgamma_r()
lgammaf_r()
lgammal_r(): None.

BUGS

In glibc 2.9 and earlier, when a pole error occurs, errno is set to EDOM; instead of the POSIX-mandated ERANGE. Since glibc 2.10, glibc does the right thing.